How am I ignoring the dictionary definition?
With all due respect if you had looked up the dictionary definition you would not ask that question, because your definition is about identity. That's not what the dictionary definition is. Not even close.
I suspect some people feel a certain class, either because that's how they were brought up or that's what they wish to be. And they then make up a definition to justify the label they give themselves as an adult.
Your class is not your accent, your desire to drink from pint glasses, what you aspire to, or what you prefer, it's not what your parents jobs were and what their financial bracket was. It's you, your job and your financial bracket. You as an adult. Not your auntie, not your grannies, not your mum, not your neighbour and not your mate. You.
But for some, this puts them in a class they don't want to be in, so they come up with another defitnion instead. Why bother? It doesn't change who or what you are and no one gives a shit. You're still going to earn the same and do the same job and live in the same house.
So what if your parents were middle class and you're working class, so what if your parents were working class and you're middle class. What difference does the label make. None. You will still live your life they way you are.